All Brutes are Subhuman: Aristotle and Ockham on Private Negation

The mediaeval logic of Aristotelian privation, represented by Ockham’sexposition of All A is non-P as All S is of a type T that is naturally P and no S isP, is critically evaluated as an account of privative negation. It is argued thatthere are two senses of privative negation: (1) an intensifier (as in subhuman),the inverse of Neoplatonic hypernegation (superhuman), which is studied inlinguistics as an operator on scalar adjectives, and (2) a (often lexicalized)Boolean complement relative to the extension of a privative negation in sense (1)(e.g. Brute). This second sense, which is the privative negation discussed inmodern linguistics, is shown to be Aristotle’s. It is argued that Ockham’sexposition fails to capture much of the logic of Aristotelian privation due tolimitations in the expressive power of the syllogistic. Keyterms: privative negation, Ockham, Aristotle, scalar adjectives, Neoplatonism.